The transition to synchronization of networked systems
arxiv(2023)
摘要
We study the synchronization properties of a generic networked dynamical
system, and show that, under a suitable approximation, the transition to
synchronization can be predicted with the only help of eigenvalues and
eigenvectors of the graph Laplacian matrix. The transition comes out to be made
of a well defined sequence of events, each of which corresponds to a specific
clustered state. The network's nodes involved in each of the clusters can be
identified, and the value of the coupling strength at which the events are
taking place can be approximately ascertained. Finally, we present large-scale
simulations which show the accuracy of the approximation made, and of our
predictions in describing the synchronization transition of both synthetic and
real-world large size networks, and we even report that the observed sequence
of clusters is preserved in heterogeneous networks made of slightly
non-identical systems.
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